smooth.ppp {spatstat} | R Documentation |
Performs spatial smoothing of numeric values observed at a set of irregular locations.
smooth.ppp(X, ..., weights = rep(1, X$n), at="pixels") markmean(X, ...) markvar(X, ...)
X |
A marked point pattern (object of class "ppp" ). |
... |
Arguments passed to density.ppp
to control the kernel smoothing and
the pixel resolution of the result. |
weights |
Optional weights attached to the observations. |
at |
String specifying whether to compute the intensity values
at a grid of pixel locations (at="pixels" ) or
only at the points of x (at="points" ).
|
The function smooth.ppp
performs spatial smoothing of numeric values
observed at a set of irregular locations. The functions
markmean
and markvar
are wrappers for smooth.ppp
which compute the spatially-varying mean and variance of the marks of
a point pattern.
Smoothing is performed by Gaussian kernel weighting. If the observed values are v[1],...,v[n] at locations x[1],...,x[n] respectively, then the smoothed value at a location u is (ignoring edge corrections)
g(u) = (sum of k(u-x[i]) v[i])/(sum of k(u-x[i]))
where k is a Gaussian kernel.
The argument X
must be a marked point pattern (object
of class "ppp"
, see ppp.object
).
The points of the pattern are taken to be the
observation locations x[i], and the marks of the pattern
are taken to be the numeric values v[i] observed at these
locations.
The numerator and denominator are computed by density.ppp
.
The arguments ...
control the smoothing kernel parameters
and determine whether edge correction is applied.
See density.ppp
.
The optional argument weights
allows numerical weights to
be applied to the data. If a weight w[i]
is associated with location x[i], then the smoothed
function is
(ignoring edge corrections)
g(u) = (sum of k(u-x[i]) v[i] w[i])/(sum of k(u-x[i]) w[i])
By default, the result is
a pixel image (object of class "im"
).
Pixel values are values of the interpolated function.
If at="points"
, the result is a numeric vector
of length equal to the number of points in x
.
Entries are values of the interpolated function at the points of x
.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
density.ppp
,
ppp.object
,
im.object
.
To perform interpolation, see the akima
package.
# Longleaf data - tree locations, marked by tree diameter data(longleaf) # Local smoothing of tree diameter Z <- smooth.ppp(longleaf) # Kernel bandwidth sigma=5 plot(smooth.ppp(longleaf, 5)) # mark variance plot(markvar(longleaf))